Question

What is the defining feature of exponential growth? a. The population is growing. b. The per capita growth rate is constant. c. The per capita growth rate increases rapidly over time. d. The per capita growth rate is very high.

Short answer

The defining feature of exponential growth is: \(b. \text{The per capita growth rate is constant.}\)

Step-by-step solution

Option a: The population is growing.

It is true that during exponential growth, the population size increases over time. However, this statement alone does not distinguish exponential growth from other types of population growth, such as logistic or linear growth. So, this is not the defining feature of exponential growth.

Option b: The per capita growth rate is constant.

In an exponential growth scenario, the per capita growth rate remains constant over time. This means that the population grows by a fixed proportion in each time unit. This is indeed the key feature of exponential growth. Therefore, this is the correct answer.

Option c: The per capita growth rate increases rapidly over time.

In exponential growth, the per capita growth rate remains constant and doesn't increase rapidly over time. Therefore, this option does not describe the defining feature of exponential growth.

Option d: The per capita growth rate is very high.

The per capita growth rate can be high or low during exponential growth, depending on the value of the constant. So, this option doesn't define the exponential growth specifically. Based on the evaluation, the defining feature of exponential growth can be found in option b.

Key concepts

Population Growth

Population growth refers to the change in the number of individuals in a given population over time. It's a central concept in understanding how communities of organisms, such as animals, plants, or even humans, expand their numbers.
Different types of population growth can occur depending on the resources available and the external environmental conditions. Key types to consider include:

• Exponential Growth: The population grows at a rate proportional to its current size, leading to rapid increases in numbers.
• Logistic Growth: The population grows rapidly at first, but then slows as it approaches the carrying capacity of the environment.
• Linear Growth: The population increases by a fixed amount over each time period.

Understanding these types helps predict population changes and manage wildlife, agricultural, and human populations effectively.

Per Capita Growth Rate

The per capita growth rate is a measure of how much each individual contributes to the overall population growth. It is a crucial factor in determining how populations change over time.
In the context of exponential growth:

• This rate remains constant, meaning that each individual contributes the same amount to the population's increase at each time step.

On the other hand, for logistic growth, the per capita rate starts high and gradually decreases as population size nears the environment's carrying capacity. This decrease occurs because competition for resources becomes stricter and growth slows down.

Logistic Growth

Logistic growth is a type of population growth characterized by an initial exponential increase that slows down as the population reaches its carrying capacity. The carrying capacity is the maximum number of individuals that the environment can support sustainably.
This growth model is very practical since it considers environmental limits, making it realistic for most natural populations. As resources become limited, the growth rate decreases, leading to a stable population size.

• Start Phase: The population grows nearly exponentially.
• Middle Phase: The growth rate slows as resources become limited.
• End Phase: Population size stabilizes at the carrying capacity.

This S-shaped curve is typical of populations that face resource limitations in real ecosystems.

Linear Growth

Linear growth describes a situation where a population increases by the same amount in each time period. Unlike exponential growth, which accelerates rapidly, linear growth is predictable and constant.
This type of growth is less common in natural populations but can occur in controlled environments such as some agricultural practices.

• Growth Rate: Constant increase per time unit.
• Predictability: Easy to model and forecast.
• Examples: Human-engineered scenarios where conditions are kept extremely stable.

Linear growth provides a simple model for educational purposes and helps to conceptually differentiate between more complex growth patterns.